Inventory Models with Alternative Delivery Lead Times, Demand Backlogging, and Priority Rules

A supplier provides several lead-time options to its customers in a periodic review inventory system. The replenishment lead time is a multiple of the inventory review cycle. Customers are classified into two groups: short lead-time customers requiring the product immediately and long lead-time customers to whom the supplier may deliver immediately or in the next cycle. We consider an inventory-commitment problem, in which the supplier allocates its on-hand inventory to these two groups of customers. When inventory runs out, the supplier backlogs orders to future cycles. Therefore, the supplier faces two problems: how the on-hand inventories are allocated between the two classes of customers and how the backlogged orders are cleared when replenishments arrive? We treat the former as an inventory-commitment problem and handle the latter with priority rules. We solve the former by dynamic programming and use three priority rules in clearing backlogs. We also explore the optimal inventory replenishment issue and evaluate the performance of each priority rule